Literature data shows that crystallisation processes of manufacturing of the various modification of aluminium oxides are not sufficiently recognised when considering the modelling and steering of different nanostructural forms. An explanation of a mechanism of a formation of characteristic not differentiated ceramic nanostructures such as peak, ridge or dendrites crystals having searched properties was presented in paper.

The inspection of the crystalline structure proofs that we usually have a contact with not smooth objects. The typical and analytical description does not reveal of the singularity structure. In relation to this the operation on the formalism leading to the description of such singularity structure can make same progress in the analysis of nanostructures as well as in steering of their construction. Author, assuming and considering conclusions resulting from Boltzman’s equations and analysing suitable energetic functional, obtains the description of the structure, which can be constructed by superposition of the elementary crystalline movements passing on not differentiated trajectories. It response on a visible crystallographic structures.

Analysing of the energy functional a formal solution has been developed which shows that its extremes described not differentiated structures. Such approach, not known so far in materials engineering, explains the formation of the mentioned crystalline nanostructures and can bring a practical meaning in research works on nanostructures in the material engineering as well as in metallography or foundry.

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